chapter 2 introduction to spreadsheet modeling. thomson/south-western 2007 © south-western/cengage...
TRANSCRIPT
Chapter 2
Introduction to Spreadsheet Modeling
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Introduction
• This book is all about spreadsheet modeling.– By the time you are finished, you will have seen some
reasonably complex—and realistic—models. – Many of you will also be transformed into Excel “power”
users.
• This chapter provides an introduction to Excel modeling and illustrates some interesting and relatively simple models.
• The chapter also covers the modeling process and includes some of the less well known, but particularly helpful, Excel tools that are available.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Basic spreadsheet modeling: Concepts and best practices
• Most mathematical models, including spreadsheet models, involve inputs, decision variables, and outputs. – The inputs have given fixed values, at least for the
purposes of the model. – The decision variables are those a decision maker
controls. – The outputs are the ultimate values of interest; they are
determined by the inputs and the decision variables.• Spreadsheet modeling is the process of entering the inputs
and decision variables into a spreadsheet and then relating them appropriately, by means of formulas, to obtain the outputs.
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Concepts and best practices continued
• After the outputs are obtained, you can proceed in several directions.– You might want to perform a sensitivity analysis to see how
one or more outputs change as selected inputs or decision variables change.
– You might want to find the values of the decision variable(s) that minimize or maximize a particular output, possibly subject to certain constraints.
– You might also want to create charts that show graphically how certain parameters of the model are related.
– These operations are illustrated with several examples in this chapter.
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Concepts and best practices continued
• You should construct your models with readability in mind, especially if the models are shared with others.
• Features that improve readability include:– A clear, logical layout to the overall model– Separation of different parts of a model, possibly across
multiple worksheets– Clear headings for different sections of the model and
for all inputs, decision variables,– and outputs– Use of range names
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Concepts and best practices continued
• Readability features continued:– Use of boldface, italics, larger font size, coloring,
indentation, and other formatting features– Use of cell comments– Use of text boxes for assumptions and explanations
• The formulas and logic in any spreadsheet model must be correct.
• Much of the power of spreadsheets derives from their flexibility.
• Plan ahead before diving in, and if your plan doesn’t look good after you start filling in the spreadsheet, revise your plan.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Cost projections
• In Example 2.2, a company wants to project its costs of producing products, given that material and labor costs are likely to increase through time.
• We build a simple model and then use Excel’s charting capabilities to obtain a graphical image of projected costs.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Breakeven analysis
• Many business problems require you to find the appropriate level of some activity.
• This might be the level that maximizes profit (or minimizes cost), or it might be the level that allows a company to break even—no profit, no loss.
• We discuss a typical breakeven analysis in Example 2.3.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Using Goal Seek
• From the data table in Example 2.3, we see that profit goes from negative to positive when the response rate is somewhere between 5% and 6%.
• Question 2 of the example asks for the exact breakeven point. This could be found with trial and error but is easy with Excel’s Goal Seek tool. Goal Seek is used to solve a single equation with a single unknown.
• In the example, the equation is Profit=0, and the single unknown is the response rate.
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Using Goal Seek continued
• In Excel terminology, the unknown is called the changing cell because we are allowed to change it to make the equation true.
• To implement Goal Seek, select Goal Seek from the What-If Analysis dropdown in the Data ribbon and fill in the resulting dialog box as shown below.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Ordering with quantity discounts and demand uncertainty
• In Example 2.4, we again attempt to find the appropriate level of some activity: how much of a product to order when customer demand for the product is uncertain.
• Two important features of this example are the presence of quantity discounts and the explicit use of probabilities to model uncertain demand.
• Except for these features, the problem is very similar to the one discussed in Example 2.1.
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Estimating the relationship between price and demand
• Example 2.5 illustrates a very important modeling concept: estimating relationships between variables by curve fitting.
• You will study this topic in much more depth in the discussion of regression in Chapter 14, but the ideas can be illustrated at a relatively low level by taking advantage of some of Excel’s useful features.
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Estimating the relationship:The functions
• The three functions have some general properties that should be noted because of their widespread applicability.
• The linear function is the easiest. – Its graph is a straight line. – When x changes by 1 unit, y change by b units. – The constant a is called the
intercept, and b is called
the slope
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Estimating the relationship:The functions continued
• The power function is a curve except in the special case where the exponent b is 1 (then it is a straight line). The shape of the curve depends primarily on the exponent b.– If b >1, y increases at an increasing rate as x increases.– If 0 < b < 1, y increases, but at a decreasing rate, as x increases.– If b < 0, y decreases as x increases.
• An important property of the power curve is that when x changes by 1%, y changes by a constant percentage, and this percentage is approximately equal to b%.– For example, if y = 100x-2.35, then every 1% increase in x leads to an
approximate 2.35% decrease in y.
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Estimating the relationship: The functions continued
• The exponential function also represents a curve whose shape depends primarily on the constant b in the exponent.– If b > 0, y increases as x increases.– If b < 0, y decreases as x increases.
• An important property of the exponential function is that if x changes by 1 unit, y changes by a constant percentage, and this percentage is approximately equal to 100 x b%.
• Another important note about the equation is that it contains e, the special number 2.7182…. In Excel, e to any power can be calculated by the EXP function.
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Estimating the relationship continued
• If we superimpose any one of these curves on the scatterplot for demand versus price, Excel will choose the best fitting curve of that type.
• Better yet if we check the Display Equation on Chart option, we see the equation of this best-fitting curve.
• Doing this for each type of curve we obtain the results in the following figures.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Best-fitting power curve
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Best-fitting exponential curve
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Estimating the relationship continued
• Each of these curves provides the best-fitting member of its “family” to the demand/price data, but which of these three is best overall?
• We answer this question by finding the mean absolute percentage error (MAPE) for each of the three curves.
• To do this, for any price in the data set and any of the three curves, we first predict demands by substituting the given price into the equation for the curve.
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Estimating the relationship continued
• The predicted demand will typically not be the same as the observed demand, so we can calculate the absolute percentage error (APE) with the general formula
• Then we average these values of the APE for any curve to get its MAPE. We will consider the curve with the smallest MAPE as the best fit overall.
• Example calculations appear in Example 2.5.
demandObserved
demandredictedPdemandObservedAPE
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Decisions involving the time value of money
• In many business situations, cash flows are received at different points in time, and a company must determine a course of action that maximizes the “value” of cash flows. Here are some examples:– Should a company buy a more expensive machine that
lasts for 10 years or a less expensive machine that lasts for 5 years?
– What level of plant capacity is best for the next 20 years?
– A company must market one of several midsize cars. Which car should it market?
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Decisions involving the time value of money continued
• To make decisions when cash flows are received at different points in time, the key concept is that the later a dollar is received, the less valuable the dollar is.
• The value of the dollar at some time in the future is given by the equation:
$1.00 x 1/(1+r) now = $1.00 a year from now• The value 1/(1+r) is called the discount factor,
and it is always less than 1.
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Decisions involving the time value of money continued
• In general, if money can be invested at annual rate r compounded each year, then $1 received t years from now has the same value as 1(1+r)t dollars received today.
• If you multiply a cash flow received t years from now by 1(1+r)t to obtain its present value, then the total of these present values over all years is called the net present value (NPV) of the cash flows.
• The rate r (usually called the discount rate) used by major corporations generally comes from some version of the capital asset pricing model.
• Example 2.6 demonstrates this concept.
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Conclusion
• The examples in this chapter provide a glimpse of things to come in later chapters. – You have seen the spreadsheet modeling approach to
realistic business problems, learned how to design spreadsheet models for readability, and explored some of Excel’s powerful tools, particularly data tables.
• In addition, at least three important themes have emerged from these examples: – relating inputs and decision variables to outputs by
means of appropriate formulas, optimization (for example, finding a “best” order quantity), and the role of uncertainty(uncertain response rate or demand).
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Summary of key management science terms
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Summary of key Excel terms
Thomson/South-Western 2007 ©South-Western/Cengage Learning © 2012Practical Management Science, 4eWinston/Albright
Summary of key Excel terms continued
End of Chapter 2